1973-03-25 — Page 19

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育教僑華頁三第張五第 日一廿月二年発

1973英文中學會考試題預習專欄

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The potential difference across

If each resistance is the same. ris the effective or equivalent. resistance,

(十二)

ther

物理科

Physics (22)

Current electricity.

We have seen that negative cherges tend to move from low to high potential while positive charges move from high to low potential. Thus whenever there 19 potential difference between

places, eg. the two ends of.

The there is a flow of charge

the wire. This flow of charges constitutes the current in the wire. The current in a wire is defined as the rate of flow of charges per unit time. If a total charge of 2 coulombs leaves. a cross-section of the ware in t second, the current in the wire

I

coul/sec.

1 coul/sec. 1s callea "ampere.

It must be noted that an ampere 19 a very large unit. Since ons electron carries a charge of 1.6 x 10.19 coul. 1 ampere of electric current requires the

flow or (1,6 x 10719)=1

- 6.25 x 1018 electrons through

a cross-section of the wire in", one second! Because of this, we define a smaller unit, the milli ampere which is one-thousandth of an ampere.

Since the discovery or electme current is much earlier than the discovery of electron theory, the current, was thought to be due to positive charge carriers. The direction of current is therefore the direction of motion of posit- ive charges. This is so-called conventional current. We now

mow that current is due to electron motion in the conductor. So the electron current, which is the true current in the wire opposite to the conventional current. However, we shall refer the term "current" to convention- al current from now on. Since a positive charge moves from high to low potential, the conventional current flows from the positive pole of a cell to the negative pole-

2. Ohms Law..

is

Ohm's law states that the current flowing between any two points in a conductor is proport- ional to the potential difference between these two points provided, that the physical conditions of the circuit under consideration is uncharged. If i represents the current flowing between the two points of a conductor maintained at a potential difference V,

then

or V = R

The constant of proportionality ris called the resistance of the. conductor between these two point: If Vis in volt and i

in amp.. then Ris in ohms. i.e. 1 ohm = 1 volt./amp.

Experiments found that the resist. ance of e length, 1 of a wire of. Cross-sectional area a are relat- ed by the equation

R

p

The constant p is called the resistivity of the material of the wire. It is expressed in. ohm-metre.

It is also found that the resistance of a metal resistor increases with temperature while carbon has its resistance decreas- es with increasing temperature. The metal resistors are therefore said to have positive temperature coefficients while carbon has a negative temperature coefficients. 3. Resistors in parallel and in

series.

Consider a number of resistan ces in parallel. (as shown in fig 1).

ra

Now consider a number of resist- ances connected in series.

Then,

or

12

Yuz

= effective resistance.

It should be noted that when resistances are in parallel, the voltage drop in each resistance. is the same while when resistances are in series, the current, în each resistance is the same and the total voltage drop is the sum of the voltage drops across in- dividual resistance. e.g.1. As in fig 3. find the current througr. each resistance and the voltage

and F5 drop in 21 13

their T2 & T4 are in series, th equivalent resistance is 500 so we can reduce the circuit to & r! as shown in fig. 4. Now I & are in parallel, their effective resistance is:

500 + 500

250 L

resan

The circuit is reduced further to as shown in fig. 5.

100V

The effective resistance, or the circuit în fig 5. is

50+250 + 500 = 800 R By Ohn's law, the current

circuit is 1 = 100 – 3a.

the

This is the current through r.

since they are all in and series. The circuit in fig 5. called the equivalent circuit of the one in fig 3.

So i = 3A is also the current

hrough

and 15 in fig 3.

ltage drop in r, 1s

The

1

☎ × 50 = 6.25 V.

The voltage drop in r

V5

voltage drop in ra

1 x 500 = 62.5 V.

100

6.25

31.25 volts

62.5

Now consider fig 4.

is the

effective resistance of r, and

r which are in parallel, 31.25V.

is the voltage drop in each resistance. Hence the current in r is

1.25 500

0.0625A.

and the current in r' 19

31.25 500

= 0.0625A.

Now I 1s the equivalent resistan- -de of r2 and r which are in

REFERENCE LIBRART

MAR 973

日期星

series, 0.0625A is the current

through each resistance. The

voltage drop in r is the voltage

drop in r2 and The voltage

arop in r2 2 is therefore equal to 400 x 0.0625 25 V.

Answers: The currents in r1, 2

rs are 0.125, 0.0625 A,

0.0625 A, 0.0625 A, and 0.125 A, respectively. The voltage drop

in r. is 6.25 V. in r2 is 25 V in r is 31.25 V. in is 6.25 and in is 62.5 V.

5

日五廿月三年三七九一曆公年二十六國民華中

4. Electrical energy and power

From the definition of volt, one volt is the potential differ- ence between two points if 1 joule of work is done in carrying. a unit positive charge between

these: points 1.e.

volt. = 1 joule or work

done per coulomb.

joule of work

1 volt.

Thus the work done in carrying a total charge of Q coul. through a potential difference of V volt iş

W = QV.

From the definition of current

we get. W VIt Joules.

This is electrical work done in a circuit carrying a current I for time t sec. from a potential difference of V volt. This work. lone is stored in the circuit as the electrical energy.

By Ohm's law, if the current is flowing through a resistance of R, the work done is

WIRt, this s is the Joule's. heat dissipation in the circuit. We may also the Ohm's law in the.

form

to get

Joules.

Thus we have three alternate forms

W = VIL =

t

Joules.

The power as defined as the rate of doing work. Thus

D = power

VI

The unit is in watt.

1 watt 1J/sec.

5 Electromotive force (EMF

The electromotive force of a generator of electricity is defin- ed as the terminal voltage of the device on open circuit condition. Notice that the term EMF applies only to generators of electricity. Chus the potential difference across a resistor is never said the EMF of the resistor because a resistor does not generate. electricity. On the other hand, the potential difference between the terminals of a cell or battery is often called its EMİ

6. Cells and batteries

Cells and batteries are devices which can generate electricity. Their detail construction and theory will be considered later. But first of all let's consider their intemal resistance. A cell or a battery has internal resist- ance arises from the resistance in the electrodes and in the electro- lyte. To reduce this resistance, a large area of electrodes should be in contact with the electrolyte Large cells will therefore have lower intemal resistance. The effect of internal resistance is o lower the terminal voltage of a cell. For example, a cell on per circuit condition (i.e. no current is drawn from the cell) has an EMF of 1.5 V. As soon as some electrical equipment is connected across the terminals of the cell, current will flow.⠀ This current flow through the internal resistance will cause voltage drop. The terminal voltage is then the difference between the EMF and the internal drop.

Exercise 2.

A bulb is rated at 120 V. 60 W. (a) How much current does it:

take?

(b) What is the bulb's resistan-

ce?

The resistance of a length 1. of a wire of cross-section a

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What is the resistan

ce of the wire made of the same material as the 1st. one Whose length is doubled and the diameter is halved of the 1st wire?

Find the equivalent resistance of the circuit in fig 6 and the voltage drop across be

Prove that

21022

for the circui

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I and

in fig 7.

Find the current in each resistor and the voltage drop across each resistor in fig 8.

162

200

6. For the circuit in 11g 9, find (a) the equivalent resistance of

the circuit,

(b) the total current drawn from

the battery.

(o) The total power alssipated.

100 v

LAMP M 100

500m

9:54

mm

402

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